1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trying to solve the Poschl-Teller potential

  1. Dec 29, 2011 #1
    Trying to solve the Poschl-Teller potential (quantum mechanics)

    1. The problem statement, all variables and given/known data
    I have a superpotential that give me 2 of the Poschl-Teller potentials.
    The superpotential is:
    W(x)=-b*cot(x)
    The Poschl-Teller potentials are:
    J(x,b)=b(b-1)/(sin(x))^2-b^2
    K(x,b)=b(b+1)/(sin(x))^2-b^2
    2. Relevant equations
    Schrodinger equation: Hψ=Eψ
    3. The attempt at a solution
    I placed the potential in Schrodinger equation (neglecting the existence of constants) and received the following equations:
    ψ''(x)+(2E-J)ψ(x)=0
    ψ''(x)+(2E-K)ψ(x)=0
    I do not know what the next step I should do
    I know I need to get to Legendre polynomial but I don't know how...
    Can anyone show me how to do it?
     
  2. jcsd
  3. Dec 29, 2011 #2
    Put [itex]u=\cos x [/itex]. Rewrite the DE in the u variable....
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trying to solve the Poschl-Teller potential
  1. Modified Poschl-Teller (Replies: 3)

Loading...